<p>Designing and implementing artificial self-organizing systems is a challenging task since they typically behave nonintuitive and only little theoretical foundations exist. Predicting a system of many components with a huge amount of interactions is beyond human skills. The currently common use of simulations for design support is not satisfying, as it is time-consuming and the results are most likely suboptimal.</p> <p>In this work, we present the derivation of an analytical, time-, and space-continuous model for a swarm of autonomous robots based on the Fokker-Planck equation. While the motion model is in most parts physically motivated, the communication model is based on a heuristic approach. A showcase application to a recently proposed scenario of collective perception in a huge swarm of robots with very limited abilities is given and the simulation results are compared to the model. Despite the high level of abstraction, the prediction discrepancies are small and the parameters can be mapped one-to-one from the model to the control algorithm. Finally, we give an outlook on the capabilities of the proposed model, discuss its limitations, and suggest an improvement that could reduce the number of empirically determined parameters.</p>